Singapore Scientific Calculator

Mathematical Function Examples

Quadratic Formula

Example: x² - 5x + 6 = 0

Solution: x = 2 or x = 3

Solve using discriminant

Trigonometry

Example: sin(30°) = sin(π/6)

Result: 0.5

Convert degrees to radians

Logarithms

Example: log(100) = 2

Natural log: ln(e) = 1

Base 10 and natural logs

Exponentials

Example: 2³ = 8

Compound: e^(ln(2)) = 2

Power and exponential functions

Compound Interest

Formula: A = P(1+r)^t

Example: $1000 at 5% for 10 years

Financial calculations

Statistics

Standard deviation: σ = √(Σ(x-μ)²/n)

Normal distribution: Bell curve

Statistical calculations

Singapore Education Context

Primary School: Basic arithmetic operations (+, -, ×, /)
Secondary School: Algebra, geometry, trigonometry
Junior College: Calculus, statistics, complex numbers
University: Advanced mathematics, engineering calculations
Professional: Financial modeling, scientific research

Common Mathematical Constants

π (Pi): 3.14159265... - Circle circumference to diameter ratio
e (Euler's number): 2.71828182... - Natural logarithm base
φ (Golden ratio): 1.61803398... - (1+√5)/2
√2: 1.41421356... - Square root of 2
√3: 1.73205080... - Square root of 3

Trigonometric Values

sin(0°) = 0, sin(30°) = 0.5, sin(45°) = √2/2, sin(60°) = √3/2, sin(90°) = 1
cos(0°) = 1, cos(30°) = √3/2, cos(45°) = √2/2, cos(60°) = 0.5, cos(90°) = 0
tan(0°) = 0, tan(30°) = 1/√3, tan(45°) = 1, tan(60°) = √3, tan(90°) = undefined
Remember: Convert degrees to radians by multiplying by π/180
Unit circle: sin²θ + cos²θ = 1

Logarithm Properties

log(ab) = log(a) + log(b): Product rule
log(a/b) = log(a) - log(b): Quotient rule
log(aⁿ) = n·log(a): Power rule
log₁₀(10) = 1, ln(e) = 1: Base logarithms
Change of base: log_b(a) = ln(a)/ln(b)

Order of Operations (PEMDAS/BODMAS)

P/B - Parentheses/Brackets: Calculate expressions in parentheses first
E/O - Exponents/Orders: Calculate powers and roots
MD - Multiplication and Division: Left to right
AS - Addition and Subtraction: Left to right
Example: 2 + 3 × 4² = 2 + 3 × 16 = 2 + 48 = 50

Scientific Notation

Format: a × 10ⁿ where 1 ≤ a < 10
Large numbers: 1,500,000 = 1.5 × 10⁶
Small numbers: 0.0015 = 1.5 × 10⁻³
Calculator display: May show as 1.5E6 or 1.5E-3
Operations: Multiply exponents when raising to power

Common Formulas

Quadratic formula: x = (-b ± √(b²-4ac)) / 2a
Distance formula: d = √((x₂-x₁)² + (y₂-y₁)²)
Compound interest: A = P(1 + r/n)^(nt)
Area of circle: A = πr²
Volume of sphere: V = (4/3)πr³

Error Handling

Division by zero: Results in "Error" or "Infinity"
Square root of negative: Not defined in real numbers
Logarithm of zero/negative: Undefined
Overflow: Numbers too large to display
Syntax errors: Check parentheses and operators

Calculator Tips

Use parentheses: Ensure correct order of operations
Check units: Degrees vs radians for trigonometry
Significant figures: Consider precision in results
Verify results: Use estimation to check answers
Save intermediate results: Use memory functions

Scientific Calculator

Function Reference

Basic Operations

Trigonometric Functions

Logarithmic Functions

Constants